What is the value of sqrt(2)(cos((7pi)/4)+isin((7pi)/4)) ?

The value of sqrt(2)(cos((7pi)/4)+isin((7pi)/4)) is 1-i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(2)(cos((7pi)/4)+isin((7pi)/4))

2 (cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4}))

1 - i

Solution steps

2 (cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4}))

Rewrite using trig identities:

cos (\frac{7 π}{4}) = \frac{2}{2}

Rewrite using trig identities:

sin (\frac{7 π}{4}) = - \frac{2}{2}

= 2 (\frac{2}{2} + i (- \frac{2}{2}))

Simplify

2 (\frac{2}{2} + i (- \frac{2}{2})) : 1 - i

= 1 - i

- 2 tan (6 0^{\circ})

cos^{2} (\frac{2 π}{5}) - sin^{2} (\frac{2 π}{5})

cos (\frac{2021 π}{4})

sec (- 15 3^{\circ})

\frac{sin ^{2} ( - π )}{sec ^{2} ( - π ) - 1}

What is the value of sqrt(2)(cos((7pi)/4)+isin((7pi)/4)) ?
The value of sqrt(2)(cos((7pi)/4)+isin((7pi)/4)) is 1-i